From Fighter to Thinker — Oliver Discovers the 3-4-5 Triangle

Oliver is a 6th grader from a small town in northeast China. He’s also a multiple-time 散打 champion — a fierce young fighter with surprising grace.

Today, in a 1-on-1 remote class, he met the Pythagorean theorem for the first time.

He started by drawing and labeling a triangle on the digital whiteboard:
2, 3, and 3.5. Then he checked:

2 * 2 + 3 * 3 = 13
3.5 * 3.5 = 12.25

He smiled and said, “Very close!”

Later, we switched gears. I showed him a fun shortcut for squaring numbers ending in 5.
He only used the first few as samples, and then spotted the pattern all by himself:

To calculate 45 * 45:
→ Take the tens digit (4), add 1 (gets 5), multiply: 4 * 5 = 20 → result: 2025

Then he did the rest without help:
55 * 55 = 3025
65 * 65 = 4225
75 * 75 = 5625
85 * 85 = 7225
95 * 95 = 9025

He verified all with his calculator — the pattern was correct.

And right before the class ended, he made a real discovery.
On his own, he found the triple: 3, 4, 5.
Then, with a gentle hint from me — “If you double the triangle’s size, the shape doesn’t change” — he explored 6, 8, 10 and 9, 12, 15.
He agreed:
“There must be infinitely many right triangles like this.”

He wrote it all by hand and by heart on the board:

3² + 4² = 5²
6² + 8² = 10²
9² + 12² = 15²

Who is this Oliver?

He’s not just a champion in martial arts —
He’s dribbled two basketballs like Steph Curry in his videos.
And now, he’s also someone who has felt the beauty of math.

All in one hour.
What a golden day.